To make the sauce, gently heat and stir together the mustard and creme fraÃ®che in a small saucepan, then turn off the heat and set aside.
Put the spinach in a colander and put in the sink. Pour over kettle-hot water to wilt, cool under cold water, squeeze out as much water as possible, then set aside.
Put the potatoes in the bottom part of a tiered steamer, just cover with water and bring to the simmer. Lay the fish fillets in the first tier of the steamer and, after the potatoes have cooked for 5 mins, sit on top, cover and steam for a further 5 mins or until the fish is cooked through. While the fish and potatoes are cooking, bring another small pan of water to the boil, add the vinegar and poach the eggs to your liking - we did ours for 2 mins.
Gently reheat the sauce and add the lemon juice and a small splash of water if it’s a little too thick. Season and stir in the chives. Lift the fish tier off the potatoes, drain the potatoes, then tip them back into the pan. Add the spinach and a drizzle of the sauce, and mix to combine. Divide the potatoes and spinach between 2 plates, sit a fillet of haddock on each and top with a poached egg. Drizzle the remaining sauce over the eggs and around the fish, and serve straight away.